Will we have problems selling items we purchased in bulk from a bankruptcy auction of the manufacturer?

You can resell the items as long as you do not engage in any activities that would lead a purchaser to believe that the trademark is yours.

Usually, a trademark owner and a manufacturer enter into an agreement that includes a trademark license - which allows the manufacturer to make the goods bearing the trademark - and the trademark owner ensures that the required quality of the goods meets its expectations - to protect the trademark. From your question - it appears that you simply purchased the goods from the bankrupt manufacturer - and NOT the trademark license. Without that license - you can be sued by the trademark owner if you sell the goods where the trademark is registered.

They might be able to stop you from selling it, depending on their relationship with the manufacturer. Since you are not getting the product from the trademark holder, I don't think you can claim the benefit of the First-sale doctrine, since the trademark holder has not actually put the product on the market. If you work out a written deal with the trademark holder, you can move forward.

Provided that the party you bought these from out of bank had the legal right to sell those trademarked goods then so do you.

This type of resale falls under the First Sale Doctrine. It allows for the resale of a product once the trademark holder puts the product on the market. The primary exception to this rule is if you are selling products that are not genuine or have been altered to such a degree that they are materially different than those originating from the trademark owner. Based upon the facts that you have specified, you're probably safe in reselling these items.

Thoughtful question. Here is an analysis. If the manufacturer had no license or authorization to use the mark in commerce neither would you. You state the third party only manufactured the goods for another entity and imply that the manufacturer may have had no rights use the TM (e.g. those rights were not attached to the goods when you purchased them). The manufacturer's rights and duties with respect to the goods will be those set forth in express or implied terms with the rights holder controlling the manufacture. As a successor in interest, you may be bound by at least some of those terms.